All Hands Meeting, 2006

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All Hands Meeting, 2006

• Title Grid Workflow Scheduling in WOSE (Workflow
  Optimisation Services for e-Science Applications)
• Authors Yash Patel, Andrew Stephen McGough and
  John Darlington

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Overview

• Multiple copies of a service with different
  performance or other user defined set of
  criteria and these services cannot be selected
  at design time because their performance is not
  known at that time.
• workflow optimisation by selecting optimal web
  services at run-time and integrating dynamic
  selection of web service into workflow

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WOSE Architecture

Our work fits here
Developed by Cardiff University
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WOSE Architecture
Our work fits here
Monitor service
Developed by Cardiff University
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Our Approach

• Previous Optimisation Framework
  Service-by-service basis approach of scheduling
  services and relies on real-time load information
  for making scheduling decisions. No QoS support
• Our Approach Provides sufficient QoS guarantee
  whilst respecting QoS requirements of workflows
  for entire lifetime of workflows and uses Queuing
  Theory Stochastic Programming approaches
  (doesnt rely on real time information)

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Our Approach

• Stochastic Programming It is a technique to
  solve optimisation problems involving uncertainty
• Stochastic Programming Deterministic
  Mathematical Programming Uncertainty
• Stochastic Programming coefficient of variables
  having probability distributions
• Deterministic Mathematical Programming
  coefficient of variables are known numbers

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Our Approach

• Formulate workflow scheduling problem as a
  2-stage stochastic program
• Scheduling program Workflow structure States
  of services (mean, variance of waiting times)
  Performance models of workflow tasks QoS
  requirements of workflow and its tasks

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Our Approach

• Why is it stochastic?
• workflow tasks need to be scheduled now
  Stage-1, whilst providing guarantee that future
  workflow tasks will still meet QoS requirements
  of workflow (uncertain) Stage-2
• Stage-2 Uncertain as demands for Grid services
  are random, service times are not deterministic,
  workflows are dynamic, services themselves may
  disappear

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Our Approach

• Formulate workflow scheduling problem as 2-stage
  stochastic program
• Stage-1 is fairly straight-forward select
  services which satisfy QoS requirements of
  workflow tasks that need to be scheduled
  immediately (now)
• Stage-2 Since coefficients of variables have
  probability distributions, we compute their
  expectations by SAA (sample average
  approximation) Shapiro et al.

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Our Approach

• Scheduling Problem
• minimisestage-1 error E(stage-2 error)
• subject to various execution, deadline, cost,
  reliability etc constraints
• E(stage-2 error) is computed using SAA problem
• Error is the penalty of failing to meet the QoS
  requirements

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Our Approach

• The variables associated with penalty (one per
  constraint) are also present in the constraints
  such as execution, cost constraints etc
• If the constraints are infeasible, it forces the
  penalty variables to bind with some value
• Hence the objective reflects a value
• The coefficients of these variables in the
  objective are the inverse of the maximum
  coefficient in the relevant constraint.

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Our Approach

• SAA Problem Solve stage-1, use its result in N
  stage-2 programs. These N programs are generated
  by sampling (Monte-Carlo or Latin Hypercube)
• Take an average value of minimised objective
  values of these N programs and the stage-1 error.
  That is SAA problem
• Stage-2 programs are similar to stage-1 programs
• Stage-1 program obtains scheduling solutions for
  workflow tasks that need to be immediately
  scheduled
• Stage-2 programs obtain for future workflow
  tasks (of course respecting constraints)

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Our Approach

• Probability distributions of variable
  co-efficients many such as waiting time for web
  services, service time for web services
• 1 stage-2 program is a joint realisation of their
  values (1 sample)
• N stage-2 programs means N samples

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Algorithm for stochastic scheduling of workflows

• Step 1 Choose sample sizes N and N N,
  iteration
• count M, tolerance e and rule to terminate
  iterations
• Step 2 Check if termination is required
• for m 1, . . .,M do
• Step 3.1 Generate a sample of size N and solve
  the SAA problem. Let the optimal objective be Om
  for corresponding iteration
• end for
• Step 3.2 Compute the average and variance as L
  and VarL (M values)
• Step 3.3 Generate a sample of size N, use one
  of the feasible stage-1 solution and solve the
  SAA problem and compute average and variance as U
  and VarU (N values)
• Step 3.4 Estimate the optimality gap (Gap L -
  U) and the variance of the gap estimator (VarGap
  VarL VarU)
• Step 3.5 If Gap and/or VarGap are large, tighten
  stage-1 QoS bounds, increase the sample sizes N
  and/or N, and return to step 2
• Step 3.6 If Gap and/or VarGap and stage-1
  objective value are small, choose stage-1
  solution and stop
• end for

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Algorithm in a nutshell

• The algorithm obtains epsilon-optimal solutions
  and sample size N guarantees that
• The algorithm ensures that QoS requirements can
  be satisfied with sufficient guarantee and
  variability of penalty is minimum
• If it is not then cost and time allocations to
  stage-1 workflow tasks are reduced so that in the
  next iteration probability of satisfying QoS
  requirements of stage-2 tasks increases

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Scheduling Strategies

• The SP (stochastic programming) scheme (similar
  to 2nd scheme) is compared with 2 traditional
  schemes
• 1st scheme Obtains scheduling solutions for all
  workflow tasks at the same time. Hence is static
• 2nd scheme Obtains scheduling solutions for
  workflow tasks dynamically, meaning as and when
  required

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Experimental Results

• 1st scheme just solves 1 ILP which obtains
  solutions respecting the QoS requirements and
  keeping the penalty to a minimum
• In the other two schemes, cost and time
  allocations to stage-1 workflow tasks initially
  is done using upper bound of the 95th confidence
  interval of execution distribution of workflow
  tasks
• In all the 3 schemes, the expected execution time
  for stage-1 workflow tasks is calculated as the
  upper bound of the 95th confidence interval of
  execution distribution of workflow task and
  waiting time distribution of services

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Experimental Results

• The SP scheme is different to 2nd scheme in the
  way the scheduling solutions are obtained
• 2nd scheme just solves 1 ILP based on the cost
  and time allocations of workflow tasks
• SP scheme obtains solutions iteratively through
  the algorithm and in the process solves numerous
  ILPs. Cost and time allocations of workflow tasks
  thus get changed, which dont in the 2nd scheme.

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Experimental Setup

• Simulation developed in SimJava
• Experimented with simple, complex and
  heterogenous workflows
• Results collected for low and high arrival rates,
  low and high CV of execution distributions of
  workflow tasks
• Different QoS requirements of workflows
• Statistics (mean response time, cost, failures,
  utilisation etc) collected for 1000 jobs
  following 500 jobs that require system initiation

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Results

• SP approach performs considerably better over
  other traditional schemes
• The SP scheme provides sufficient QoS guarantee
  over the entire life-cycle of workflows
• The scheme performs better particularly when
  workflow complexity and heterogeneity are high
• At both low and high arrival rates of workflows
  the SP scheme is a winner
• Average utilisation of services increase in the
  SP scheme

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Future Work

• Experiment with workflows having slack periods
• Enhance the scheduling model (more constraints
  and more realistic model of web services)
• Thank You